Xiangsen Qin

activity

20242026

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4 papers · 1 filter

math.CV2024

Uniform estimates of Green functions and Sobolev-type inequalities on real and complex manifolds

Fusheng Deng, Gang Huang, Xiangsen Qin

We prove certain $L^{p}$ Sobolev-type and Poincaré-type inequalities for functions on real and complex manifolds for the gradient operator $\nabla$ , the Laplace operator $Δ$ , and the…

math.CV2024

A bridge connecting convex analysis and complex analysis and $L^{2}$ -estimate of $d$ and $\partial ˉ$

Fusheng Deng, Jinjin Hu, Weiwen Jiang +1

We propose a way to connect complex analysis and convex analysis. As applications, we derive some results about $L^{2}$ -estimate for $d$ -equation and prove some curvature positivity…

math.CV2024

Curvature formulas and curvature strict positivity of direct image bundles

Xiangsen Qin

In this paper, we consider the curvature strict positivity of direct image bundles (vector bundles) associated to a strictly pseudoconvex family of bounded domains.The main result…

math.CV2024

$\partial ˉ$ Sobolev-type inequality and an improved $L^{2}$ -estimate of $\partial ˉ$ on bounded strictly pseudoconvex domains

Fusheng Deng, Weiwen Jiang, Xiangsen Qin

We prove several Sobolev-type inequalities related to the $\partial ˉ$ -operator on bounded domains in $C^{n}$ , which can be viewed as a $\partial ˉ$ -version of the class…

Uniform estimates of Green functions and Sobolev-type inequalities on real and complex manifolds

A bridge connecting convex analysis and complex analysis and L2-estimate of d and ∂ˉ

Curvature formulas and curvature strict positivity of direct image bundles

∂ˉ Sobolev-type inequality and an improved L2-estimate of ∂ˉ on bounded strictly pseudoconvex domains

A bridge connecting convex analysis and complex analysis and $L^{2}$ -estimate of $d$ and $\partial ˉ$

$\partial ˉ$ Sobolev-type inequality and an improved $L^{2}$ -estimate of $\partial ˉ$ on bounded strictly pseudoconvex domains